Let R be a relation on the set Z of all integers defined as

Given: $R$ is the equivalence relation on the set $Z$ of integers defined as $(x, y) \in R \Leftrightarrow x-y$ is divisible by 2 .

To find the equivalence class [1], we put y = 1 in the given relation and find all the possible values of x.

Thus,

$R=\{(x, 1): x-1$ is divisible by 2$\}$

$\Rightarrow x-1$ is divisible by 2

$\Rightarrow x=\pm 1, \pm 3, \pm 6, \pm 9, \ldots .$

Therefore, equivalence class $[0]=\{\pm 1, \pm 3, \pm 6, \pm 9, \ldots .\}$c

Hence, the equivalence class [1] is $\{\underline{\pm} 1, \pm 3, \pm 6, \pm 9, \ldots\} .$